Approximate consensus is an important building block for distributed systems, used overtly or implicitly in applications as diverse as formation control, sensor fusion, and synchronization. Laplacian-based consensus, the current dominant approach, is extremely accurate and resilient, but converges slowly. Comparing Laplacian-based consensus to exact consensus algorithms, relaxing the requirements for accuracy and resilience should enable a spectrum of algorithms that incrementally tradeoff accuracy and/or resilience for speed. This manuscript demonstrates that may be so by beginning to populate this spectrum with a new approach to approximate consensus, Power-Law-Driven Consensus (PLD-consensus), which accelerates consensus by sending values across long distances using a self-organizing overlay network. Both a unidirectional and bidirectional algorithm based on this approach are studied. Although both have the same asymptotic O(diameter) convergence time (vs. O(diameter 2) for Laplacian-based), unidirectional PLD-consensus is faster and more resilient than bidirectional PLD-consensus, but exhibits higher variance in the converged value.

Pervasive systems are intended to make use of services and components that they encounter in their environment. Such systems are naturally spatial in that they can only be understood in terms of the ways in which components meet and interact in space. Rather than treating spatiality separately from system components, researchers are starting to develop computational models in which the entire structure of a pervasive system is modelled and constructed using an explicit spatial model, supporting multi-level spatial reasoning, and adapting autonomously to spatial interactions. In this paper, we review current and emerging models of spatial computing for pervasive ecosystems, and highlight some of the trends that will guide future research.

This paper presents a novel concept of a Spatially Aware Graph Store, which realizes a Graph Store on top of a spatial computer architecture to manage graphs in one, two or three physical dimensions. In this environment, the physical distance between graph nodes strongly affects graph traversal performance. Consequently, a Spatially Aware Graph Store needs to minimize these distances to operate efficiently. We show that this minimization can be achieved in two ways. First, by increasing the dimensionality of the spatial computer and second by applying optimization methods. For the latter, this work introduces a novel Mid Point Optimization method to quickly optimize large real-world knowledge networks by rearranging nodes in a way that distances between linked nodes are reduced. In addition, a Local Optimization method is subsequently applied to refine the result. Finally, the Node Decomposition method is presented that splits nodes with many edges into several smaller nodes to achieve a further reduction of distances between linked nodes.

Our results show that the overall distances between nodes can be reduced by three orders of magnitude for 3D in comparison to one-dimensional (1D) Spatially Aware Graph Stores. The suggested Mid Point Optimization method achieves a reduction by another order of magnitude. In a 3D spatial computer, Local Optimization is capable of reducing distances by another 20%. However, in 1D and 2D spatial computers it becomes a prohibitive time consuming method. Finally, the Node Decomposition enables an additional distance reduction by 40% in Scale Free Graph Data sets.

The Resource Description Framework (RDF) is a flexible model for representing information about resources on the Web. As a W3C (World Wide Web Consortium) Recommendation, RDF has rapidly gained popularity. With the widespread acceptance of RDF on the Web and in the enterprise, a huge amount of RDF data is being proliferated and becoming available. Efficient and scalable management of RDF data is therefore of increasing importance. RDF data management has attracted attention in the database and Semantic Web communities. Much work has been devoted to proposing different solutions to store RDF data efficiently. This paper focusses on using relational databases and NoSQL (for ‘not only SQL (Structured Query Language)’) databases to store massive RDF data. A full up-to-date overview of the current state of the art in RDF data storage is provided in the paper.